Learn Polish: Mieszkamy nad rzeką. - We live by the river.

In Polish, you usually don't need to use subject pronouns like my (we) because the verb ending already tells you who is doing the action. The -my ending in mieszkamy clearly means "we live".

Doesn't the word nad usually mean "above" or "over"?

Yes, it does! However, in Polish, when you talk about being located near a body of water (like a river, lake, or sea), you use nad. In this context, it translates to "by", "at", or "on the bank of".

Why does the word for river end in an -ą (rzeką) instead of an -a (rzeka)?

The preposition nad requires the noun that follows it to change its ending when talking about a fixed location (this is called the Instrumental case). For feminine nouns like rzeka, the -a ending changes to an -ą.

Could I use the verb żyjemy instead of mieszkamy to say "we live" here?

Not quite! While both mean "to live", mieszkać specifically means to reside or have your home somewhere, which is what you want here. Żyć is about the state of being alive. Saying żyjemy nad rzeką would sound a bit dramatic, more like "we survive by the river".